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titleOverview

The Square 2D case involves thermal diffusion in a horizontal flow on a unit square domain. The numerical heat flux at the bottom boundary (y=0) is checked with the analytical heat flux to a specified tolerance. All boundaries are set to a thermal condition which is a function of x and y, and the initial condition is set to 1.

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titleTemperature Distribution:

  • Horizontal Flow
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  • Boundary Condition:
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    • Non-dimensional viscosity:
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    titleFlow Conditions:
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    titleSolver Parameters:
    • Equation Set: Scalar 2D
    • Nonlinear Solver: Newton
    • Basis Type: Hierarchical
    • Initial/Max CFL: 1030
    • Target residual: 10-11
    • Preconditioning:
    • Type: ILU (Left)
    • Reordering: MDF
    • Outer GMRES iterations (# restarts): 20
      • Inner GMRES iterations (# Krylov vectors): 200

    Tested Outputs

    L2 error (compared to an exact solution function)

    • Numerical heat flux on inner bottom boundary (y=0)
    • Exact heat flux error on inner boundary
    • L∞ of the exact heat flux error
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    titleFlow Conditions:
    • Horizontal Flow
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    • Boundary Condition:
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    • Non-dimensional viscosity:
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    Case Specific Details

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    titleCase 1 (Non-AdaptiveILU):
    • Solution Order: 2: 3
    • Target residual: 10-11
    • Preconditioning:
      • Type: ILU (Left)
      • Reordering: MDF
      • Outer GMRES iterations (# restarts): 20
      • Inner GMRES iterations (# Krylov vectors): 200
    • Iterations to solve: 2
    • All outputs Heat flux output tested to a tolerance of 10-12

    Job File:
    Square_Scalar2d_CircleBoundaryLayerGMRES_ILU

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    titleCase 1 Jacobi


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    titleCase 2 (AdaptiveJacobi):
    • Solution Order = 1
    • Additional tested outputs: Heat flux adjoint residual
    • Adaptation parameters:
      • Adaptation Iterations: 2
      • Adaptation Method: Fixed fraction
      • Output Adapted: Heat flux
      • Anisotropy Method: Hessian
    • : 0
    • Target residual: 10-12
    • Preconditioning:
      • Type: Jacobi (Left)
      • Reordering: MDF
      • Outer GMRES iterations (# restarts): 20
      • Inner GMRES iterations (# Krylov vectors): 200
    • Iterations to solve: 2
    • Heat flux output
    • Iterations to solve on each mesh: 2
    • All outputs tested to a tolerance of 10-1012

    Job File:
    Square_Scalar2d_CircleBoundaryLayerGMRES_AdaptJacobi

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    titleCase 2 ILU:


    Case Details

    Square_Scalar2d_GMRES_ILU

    ...